The invention generally relates to data processing and compression and more particularly to a new technique for representing data more efficiently, referred herein as a digital Ridgelet transform.
As the amount of information that is available or needed increases, the need for more efficient ways to represent the information increase as well. The goal of data compression is to more efficiently represent information. The information can be in a variety of forms, such as speech, images, text, video, music, etc.
In particular, there has been a very rapid increase in the amount of information stored as images, especially remotely sensed images from weather and other satellites, and medical images such as CAT scans, magnetic resonance images, and mammograms. A pixel representation of an image is a very inefficient representation due to the redundancies in the image. These images must typically be remotely accessible by Doctors and other individuals, and thus, must be transmitted over networks or other links. If the image can be more efficiently represented, the image can be stored using less memory and can be more quickly transmitted over a data or computer network or over a transmission link, etc. in less time or transmitted using less bandwidth.
A number of different transforms, such as Discrete Cosine Transform and Wavelet Transform, etc., have been used in attempt to compress data. While providing data compression, many of these transform techniques can introduce losses or errors which can significantly distort the image. Many current transform or compression techniques calculate a transform coefficient across a block of pixels or sample values. As a result, the lines in the reconstructed image are typically imprecise and are jagged or rough. Such a jagged or imprecise line in the reconstructed image can be a problem where doctors or scientists must precisely identify the boundary or line between two objects in an image.
Therefore, a need exists for a technique to efficiently represent or compress data while allowing a more accurate reconstructed image, particularly along lines in the image.
According to an embodiment of the present invention, a technique which is called a Ridgelet transform is disclosed for more efficiently representing information. According to an embodiment of the present invention, original data samples (e.g., in the time domain)are received. The original data samples are then transformed into frequency domain values provided in Cartesian coordinates using a Fourier transform or other technique. The frequency domain values provided in Cartesian coordinates are then transformed to digital polar coordinates (provided in a digital polar grid). Because the polar grid is non-uniform, the polar coordinate values are weighted or normalized. A Wavelet transform is performed on values derived from the frequency domain values provided in digital polar coordinates to generate Wavelet coefficients (or Ridgelet coefficients). Next a thresholding process can be performed. According to the thresholding process, the Wavelet coefficients are filtered to select a group of larger Wavelet coefficients and discard the remaining Wavelet coefficients (e.g., select those coefficients which are greater than a threshold, and discard the remaining coefficients). Many of the Ridgelet coefficients have a value that is negligible compared to some of the larger Ridgelet coefficients. The result is a representation of the original information that is much more efficient or compressed, while allowing an accurate reconstruction of the original information therefrom. The Ridgelet transform of the present invention can advantageously be used in a wide variety of applications including compression (such as image or data compression), statistical estimation (including noise removal, edge detection and feature detection), scientific or mathematical computing, and the like.